An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is $16$ $16$ , the cap's height is $2$ $2$ , and the cap's radius is $5$ $5$ . What is the object's volume?

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Answer 1 · 2018-08-04T13:24:51

1097.37 cu. I would review my answer and improve and make corrections, if any. Please do not edit this answer.

From the dimensions of the spherical cap, the semi-angle that it

subtends at the center of its sphere,

$α$ $alpha$ rad $= arcsin (\frac{4}{5}) = 0.9273$ $= arcsin (4/5) = 0.9273$ ,

The side length

of the square top of the prism is 2 (4 ) = 8.

The entire volume = Volume of the cap + volume of the prism

= (( volume of the cone + volume of the

spherical cap ) - volume of the cone) + volume of the prism

$= (\frac{4}{3} (5^{3}) α sin α - \frac{1}{3} π (4^{2}) (3)) + (16) (8^{2}$ $= ( 4/3 (5^3)alpha sin alpha - 1/3 pi (4^2)(3)) + (16)(8^2$ )

$= \frac{4}{3} (5^{3}) (0.9273) (\frac{4}{5}) - \frac{1}{3} (3.1416) (9) (3)$ $= 4/3(5^3) ( 0.9273)( 4/5 ) - 1/3 (3.1416)(9)(3)$

#= 1097.37 cu

An object is made of a prism with a spherical cap on its square shaped top. The cap's base has a diameter equal to the length of the top. The prism's height is 16 16 , the cap's height is 22 , and the cap's radius is 55 . What is the object's volume?